1. **Problem:** Find the maturity value of 20000 invested for 3 years at 8% compounded quarterly, and find the compound interest. 2. **Formula:** The maturity value $A$ for compound interest is given by: $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $P$ is the principal amount (20000), - $r$ is the annual interest rate (0.08), - $n$ is the number of compounding periods per year (4 for quarterly), - $t$ is the time in years (3). 3. **Calculate:** - Compute the periodic interest rate: $\frac{r}{n} = \frac{0.08}{4} = 0.02$ - Compute total compounding periods: $nt = 4 \times 3 = 12$ - Calculate maturity value: $$A = 20000 \times (1 + 0.02)^{12} = 20000 \times (1.02)^{12}$$ 4. **Evaluate:** Calculate $(1.02)^{12}$: $$ (1.02)^{12} \approx 1.26824179 $$ So, $$ A \approx 20000 \times 1.26824179 = 25364.84 $$ 5. **Compound Interest:** Compound interest $CI = A - P = 25364.84 - 20000 = 5364.84$ 6. **Answer:** - Maturity value is approximately **25364.84** - Compound interest is approximately **5364.84**